Equilibrium inner radial crack in a pipe section with an external protective coating

Abstract

The problem of plane deformation of the elastic ring with an inner radial cut is considered. On the inner edge of the ring hydrostatic pressure affected. The outer boundary is reinforced with a thin flexible coating, the outer boundary of it is free. As a coating model used special boundary conditions are formulated on the basis of the asymptotic analysis of the exact solution of the elasticity problem for the ring. It is difficult to find a range of geometrical and physical parameters of the problem analytically. That's why a series of numerical experiments using FEM package carried out. In particular, it was found that the error of the accepted model increases with the coating hardness and thickness. Discontinuous solution method technology in the Fourier series implemented. The boundary conditions on the crack faces satisfied. As a result of summation of series, the problem reduces to the solution of a singular integral equation for the derivative crack expanding function. The singular part is a Cauchy kernel and corresponds to the limiting classical case. A regular part of the kernel depends on the geometrical and physical parameters of the problem. The convergence of the obtained series investigated. The solution of the integral equation is constructed by collocation method as a linear combination of basis functions. Of course we taking into account the characteristic peaks in the vicinity of the crack. A first kind Chebyshev polynomials are used. Reduced stress intensity factor as an influence factor established. Qualitative and quantitative features of effect of the material and coating thickness on the intensity of the stresses in the vicinity of the crack tip established.